What is the equation of the parabola that has a vertex at # (5, 2) # and passes through point # (6,9) #?

1 Answer
Anjali G
Aug 10, 2018

#f(x) = 7(x-5)^2+2#

Explanation:

Vertex form of a parabola with a vertex at #(5,2)#
#f(x) = a(x-5)^2+2#

To find the value of #a#, think about how the y increases in relation to the vertex of the parabola.

Start from the vertex, move right 1 unit. If #a = 1#, then the parabola would intersect #(5 color(blue)(+1) , 2 color(green)(+1) )#. In our case, however, the parabola must intersect #(5 color(blue)(+1) , 2 color(red)(+7) )#.

Therefore, our #a# value is equal to #frac{color(red)(7)}{color(green)(1)} = 7#

#f(x) = 7(x-5)^2+2#

graph{7(x-5)^2+2 [-2.7, 17.3, -2.21, 7.79]}

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